The method and the results are on the angular momentum lab. Do the analysis yourself first, then check the answers below.
Quick answer: Angular momentum is the rotational equivalent of momentum: L = Iω for a rigid body, or L = r × p for a particle. These answers go with the AP Physics C lab on angular momentum: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample data in the results table. Your own values will differ slightly, but the ratio of the accelerations should stay close to 4/3, and your β values should be near 0.5 and 1. Always state the uncertainty with the final result.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 6
Solid rod: (1.76 + 1.73 + 1.78 + 1.75 + 1.74) / 5 = 1.752 s. Range 1.73–1.78 s, so half-range 0.025 s. The mean time is 1.75 ± 0.03 s.
Question 2 Acceleration
Solid: a = 2.00 / 1.752² = 0.652 m/s². Tube: a = 2.00 / 2.028² = 0.486 m/s². The time uncertainty is 0.025/1.752 = 1.4 %, and a ∝ t⁻², so the uncertainty in a is 2.9 %.
Question 3 Experimental shape factor
β = g sinθ / a − 1. Solid: 0.981 / 0.652 − 1 = 0.505, so β = 0.51. Tube: 0.981 / 0.486 − 1 = 1.02, so β = 1.02.
Question 4 Compare with theory
Theory gives 1/2 for a solid cylinder and about 1 for a thin-walled tube. The measured 0.51 and 1.02 agree with theory to within about 2 %, well inside the uncertainty.
Question 5 Ratio of accelerations
Measured: 0.652 / 0.486 = 1.34. Theory: (1 + 1) / (1 + 0.5) = 1.33. The agreement is within 1 %.
Question 6 Effect of mass
Mass cancels in a = g sinθ / (1 + β), so the time would be unchanged, provided the shape stays the same.
Question 7 Improving the lab
Use light gates or video analysis to time more accurately, and use a longer, steeper ramp so the times are larger compared with human reaction time. Both reduce the percentage error in t.
